This research was conducted for the purpose of assessing the practicality of introducing the Discourse Intonation theory in the Language Institute of Al-Baath University, Syria. Using a case study tradition, the various features of the theory were presented over a number of sessions, thus providing the participants of the study, being advanced teacher-learners, with a thorough treatment of these features for the purpose of examining their cognitive and affective reception of each of these features. The final purpose was to see if these participants would be able to pedagogically deal with these features and find them relevant to their own self-development, as well as to see if the Discourse Intonation theory is seen, from a teaching point of view, to have a place at the Language Centre. The results were encouraging. When the participants sat the course, they found it difficult sometimes to grasp some of the rules, and they also encountered some occasional difficulty in doing listening and speaking tasks, although this difficulty was not consistent, and often differed from one feature to the other. Although the participants managed to demonstrate at least a basic understanding of the rules stated in the course, they were less consistent in their ability to explicitly describe how the new rules would relate to the English language in general terms. However, the findings were promising because they contained evidence to the effect that the participants‘ thinking of intonation was stimulated, and their critical reception of DI meant that they had already taken the first step towards actively benefiting from the course, thus redefining the meaning of ‗benefit‘ when it comes to instruction on intonation. This optimism is further supported by the fact that three participants thought that the theory would deserve a place for an explicit treatment at Language Institute. This is implied by the various recommendations that the participants suggested for successfully approaching the teaching of Discourse Intonation. The suggested approach, characterized by anticipating learning difficulties and thinking of solutions, indicates an actively critical perspective and a wellinformed position which, with its positive evaluation of the place of this theory in pedagogy, shows advances on the many negative teacher attitudes expressed in the literature. The research, departing from these findings, offered some suggestions for both further teaching and further research on the teachability of Discourse Intonation, in the hope of having gone a step further in our understanding of the relationship of Discourse Intonation to pedagogy.